5. The joint probability mass function of the two random variables X and Y with values in {1, 2, 3} and {0, 1,2}, respectively, is given by the following table: X\Y 0 1 2 1 0 1/9 0 2 1/3 2/9 1/9 3 0 1/9 1/9 (a) Find the conditional probability mass function of X given Y = y. (b) Find the conditional expectation E[X|Y = y] for y = 0,1,2.

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